{"id":"https://openalex.org/W3155673956","doi":"https://doi.org/10.1007/s00373-021-02318-5","title":"A Proof of a Dodecahedron Conjecture for Distance Sets","display_name":"A Proof of a Dodecahedron Conjecture for Distance Sets","publication_year":2021,"publication_date":"2021-04-17","ids":{"openalex":"https://openalex.org/W3155673956","doi":"https://doi.org/10.1007/s00373-021-02318-5","mag":"3155673956"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-021-02318-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-021-02318-5","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010500327","display_name":"Hiroshi Nozaki","orcid":"https://orcid.org/0000-0001-8039-1010"},"institutions":[{"id":"https://openalex.org/I39018119","display_name":"Aichi University of Education","ror":"https://ror.org/03m964n84","country_code":"JP","type":"education","lineage":["https://openalex.org/I39018119"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi Nozaki","raw_affiliation_strings":["Department of Mathematics Education, Aichi University of Education, 1 Hirosawa, Igaya-cho, Kariya, Aichi, 448-8542, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Aichi University of Education, 1 Hirosawa, Igaya-cho, Kariya, Aichi, 448-8542, Japan","institution_ids":["https://openalex.org/I39018119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069560709","display_name":"Masashi Shinohara","orcid":"https://orcid.org/0000-0001-8444-0983"},"institutions":[{"id":"https://openalex.org/I171494771","display_name":"Shiga University","ror":"https://ror.org/01vvhy971","country_code":"JP","type":"education","lineage":["https://openalex.org/I171494771"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masashi Shinohara","raw_affiliation_strings":["Faculty of Education, Shiga University, 2-5-1 Hiratsu, Otsu, Shiga, 520-0862, Japan"],"raw_orcid":"https://orcid.org/0000-0001-8444-0983","affiliations":[{"raw_affiliation_string":"Faculty of Education, Shiga University, 2-5-1 Hiratsu, Otsu, Shiga, 520-0862, Japan","institution_ids":["https://openalex.org/I171494771"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069560709"],"corresponding_institution_ids":["https://openalex.org/I171494771"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.1884,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.45494695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"37","issue":"5","first_page":"1585","last_page":"1603"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8531445264816284},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8274683356285095},{"id":"https://openalex.org/keywords/dodecahedron","display_name":"Dodecahedron","score":0.8238582611083984},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6806033849716187},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6347609162330627},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6121108531951904},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5535168051719666},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5164635181427002},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48724547028541565},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.45486611127853394},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43270355463027954},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.26796919107437134},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10748842358589172}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8531445264816284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8274683356285095},{"id":"https://openalex.org/C94239619","wikidata":"https://www.wikidata.org/wiki/Q178296","display_name":"Dodecahedron","level":2,"score":0.8238582611083984},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6806033849716187},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6347609162330627},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6121108531951904},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5535168051719666},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5164635181427002},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48724547028541565},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.45486611127853394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43270355463027954},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.26796919107437134},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10748842358589172},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-021-02318-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-021-02318-5","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1587724548","display_name":"Research on extremal combinatorics by Ramsey methods","funder_award_id":"18K03396","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6155034625","display_name":"Delsarte theory for infinite association schemes","funder_award_id":"19K03445","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8397348179","display_name":"Noncommutative association schemes, coherent algebras, their irreducible decompositions and applications","funder_award_id":"20K03527","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1572364899","https://openalex.org/W1572708899","https://openalex.org/W1620653847","https://openalex.org/W1964607221","https://openalex.org/W1976677460","https://openalex.org/W1979758769","https://openalex.org/W2020003328","https://openalex.org/W2021036646","https://openalex.org/W2033418922","https://openalex.org/W2038645106","https://openalex.org/W2048741530","https://openalex.org/W2059472015","https://openalex.org/W2072305548","https://openalex.org/W2101796151","https://openalex.org/W2138033161","https://openalex.org/W2144778768","https://openalex.org/W2259854082","https://openalex.org/W2556959701","https://openalex.org/W2889519599","https://openalex.org/W2899036773","https://openalex.org/W2963295388","https://openalex.org/W3000276910","https://openalex.org/W3000812109","https://openalex.org/W3105385860","https://openalex.org/W4241301183","https://openalex.org/W4245083374","https://openalex.org/W4298236575","https://openalex.org/W6831519853"],"related_works":["https://openalex.org/W2090152127","https://openalex.org/W1965169884","https://openalex.org/W3125580510","https://openalex.org/W2008939113","https://openalex.org/W14679004","https://openalex.org/W1566651525","https://openalex.org/W2977652649","https://openalex.org/W2318206461","https://openalex.org/W37157938","https://openalex.org/W2105228010"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
